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Néron Models [[electronic resource] /] / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Néron Models [[electronic resource] /] / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Autore Bosch Siegfried
Edizione [1st ed. 1990.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (X, 328 p.)
Disciplina 516.35
Collana Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Soggetto topico Algebraic geometry
Algebraic Geometry
ISBN 3-642-51438-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. What Is a Néron Model? -- 1.1 Integral Points -- 1.2 Néron Models -- 1.3 The Local Case: Main Existence Theorem -- 1.4 The Global Case: Abelian Varieties -- 1.5 Elliptic Curves -- 1.6 Néron’s Original Article -- 2. Some Background Material from Algebraic Geometry -- 2.1 Differential Forms -- 2.2 Smoothness -- 2.3 Henselian Rings -- 2.4 Flatness -- 2.5 S-Rational Maps -- 3. The Smoothening Process -- 3.1 Statement of the Theorem -- 3.2 Dilatation -- 3.3 Néron’s Measure for the Defect of Smoothness -- 3.4 Proof of the Theorem -- 3.5 Weak Néron Models -- 3.6 Algebraic Approximation of Formal Points -- 4. Construction of Birational Group Laws -- 4.1 Group Schemes -- 4.2 Invariant Differential Forms -- 4.3 R-Extensions of K-Group Laws -- 4.4 Rational Maps into Group Schemes -- 5. From Birational Group Laws to Group Schemes -- 5.1 Statement of the Theorem -- 5.2 Strict Birational Group Laws -- 5.3 Proof of the Theorem for a Strictly Henselian Base -- 6. Descent -- 6.1 The General Problem -- 6.2 Some Standard Examples of Descent -- 6.3 The Theorem of the Square -- 6.4 The Quasi-Projectivity of Torsors -- 6.5 The Descent of Torsors -- 6.6 Applications to Birational Group Laws -- 6.7 An Example of Non-Effective Descent -- 7. Properties of Néron Models -- 7.1 A Criterion -- 7.2 Base Change and Descent -- 7.3 Isogenies -- 7.4 Semi-Abelian Reduction -- 7.5 Exactness Properties -- 7.6 Weil Restriction -- 8. The Picard Functor -- 8.1 Basics on the Relative Picard Functor -- 8.2 Representability by a Scheme -- 8.3 Representability by an Algebraic Space -- 8.4 Properties -- 9. Jacobians of Relative Curves -- 9.1 The Degree of Divisors -- 9.2 The Structure of Jacobians -- 9.3 Construction via Birational Group Laws -- 9.4 Construction via Algebraic Spaces -- 9.5 Picard Functor and Néron Models of Jacobians -- 9.6 The Group of Connected Components of a Néron Model -- 9.7 Rational Singularities -- 10. Néron Models of Not Necessarily Proper Algebraic Groups -- 10.1 Generalities -- 10.2 The Local Case -- 10.3 The Global Case.
Record Nr. UNINA-9910480014503321
Bosch Siegfried  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Néron Models [[electronic resource] /] / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Néron Models [[electronic resource] /] / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Autore Bosch Siegfried
Edizione [1st ed. 1990.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (X, 328 p.)
Disciplina 516.35
Collana Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Soggetto topico Algebraic geometry
Algebraic Geometry
ISBN 3-642-51438-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. What Is a Néron Model? -- 1.1 Integral Points -- 1.2 Néron Models -- 1.3 The Local Case: Main Existence Theorem -- 1.4 The Global Case: Abelian Varieties -- 1.5 Elliptic Curves -- 1.6 Néron’s Original Article -- 2. Some Background Material from Algebraic Geometry -- 2.1 Differential Forms -- 2.2 Smoothness -- 2.3 Henselian Rings -- 2.4 Flatness -- 2.5 S-Rational Maps -- 3. The Smoothening Process -- 3.1 Statement of the Theorem -- 3.2 Dilatation -- 3.3 Néron’s Measure for the Defect of Smoothness -- 3.4 Proof of the Theorem -- 3.5 Weak Néron Models -- 3.6 Algebraic Approximation of Formal Points -- 4. Construction of Birational Group Laws -- 4.1 Group Schemes -- 4.2 Invariant Differential Forms -- 4.3 R-Extensions of K-Group Laws -- 4.4 Rational Maps into Group Schemes -- 5. From Birational Group Laws to Group Schemes -- 5.1 Statement of the Theorem -- 5.2 Strict Birational Group Laws -- 5.3 Proof of the Theorem for a Strictly Henselian Base -- 6. Descent -- 6.1 The General Problem -- 6.2 Some Standard Examples of Descent -- 6.3 The Theorem of the Square -- 6.4 The Quasi-Projectivity of Torsors -- 6.5 The Descent of Torsors -- 6.6 Applications to Birational Group Laws -- 6.7 An Example of Non-Effective Descent -- 7. Properties of Néron Models -- 7.1 A Criterion -- 7.2 Base Change and Descent -- 7.3 Isogenies -- 7.4 Semi-Abelian Reduction -- 7.5 Exactness Properties -- 7.6 Weil Restriction -- 8. The Picard Functor -- 8.1 Basics on the Relative Picard Functor -- 8.2 Representability by a Scheme -- 8.3 Representability by an Algebraic Space -- 8.4 Properties -- 9. Jacobians of Relative Curves -- 9.1 The Degree of Divisors -- 9.2 The Structure of Jacobians -- 9.3 Construction via Birational Group Laws -- 9.4 Construction via Algebraic Spaces -- 9.5 Picard Functor and Néron Models of Jacobians -- 9.6 The Group of Connected Components of a Néron Model -- 9.7 Rational Singularities -- 10. Néron Models of Not Necessarily Proper Algebraic Groups -- 10.1 Generalities -- 10.2 The Local Case -- 10.3 The Global Case.
Record Nr. UNINA-9910789209803321
Bosch Siegfried  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Néron Models / / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Néron Models / / by Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud
Autore Bosch Siegfried
Edizione [1st ed. 1990.]
Pubbl/distr/stampa Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Descrizione fisica 1 online resource (X, 328 p.)
Disciplina 516.35
Collana Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Soggetto topico Geometry, Algebraic
Algebraic Geometry
ISBN 9783642514388
3642514383
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto 1. What Is a Néron Model? -- 1.1 Integral Points -- 1.2 Néron Models -- 1.3 The Local Case: Main Existence Theorem -- 1.4 The Global Case: Abelian Varieties -- 1.5 Elliptic Curves -- 1.6 Néron’s Original Article -- 2. Some Background Material from Algebraic Geometry -- 2.1 Differential Forms -- 2.2 Smoothness -- 2.3 Henselian Rings -- 2.4 Flatness -- 2.5 S-Rational Maps -- 3. The Smoothening Process -- 3.1 Statement of the Theorem -- 3.2 Dilatation -- 3.3 Néron’s Measure for the Defect of Smoothness -- 3.4 Proof of the Theorem -- 3.5 Weak Néron Models -- 3.6 Algebraic Approximation of Formal Points -- 4. Construction of Birational Group Laws -- 4.1 Group Schemes -- 4.2 Invariant Differential Forms -- 4.3 R-Extensions of K-Group Laws -- 4.4 Rational Maps into Group Schemes -- 5. From Birational Group Laws to Group Schemes -- 5.1 Statement of the Theorem -- 5.2 Strict Birational Group Laws -- 5.3 Proof of the Theorem for a Strictly Henselian Base -- 6. Descent -- 6.1 The General Problem -- 6.2 Some Standard Examples of Descent -- 6.3 The Theorem of the Square -- 6.4 The Quasi-Projectivity of Torsors -- 6.5 The Descent of Torsors -- 6.6 Applications to Birational Group Laws -- 6.7 An Example of Non-Effective Descent -- 7. Properties of Néron Models -- 7.1 A Criterion -- 7.2 Base Change and Descent -- 7.3 Isogenies -- 7.4 Semi-Abelian Reduction -- 7.5 Exactness Properties -- 7.6 Weil Restriction -- 8. The Picard Functor -- 8.1 Basics on the Relative Picard Functor -- 8.2 Representability by a Scheme -- 8.3 Representability by an Algebraic Space -- 8.4 Properties -- 9. Jacobians of Relative Curves -- 9.1 The Degree of Divisors -- 9.2 The Structure of Jacobians -- 9.3 Construction via Birational Group Laws -- 9.4 Construction via Algebraic Spaces -- 9.5 Picard Functor and Néron Models of Jacobians -- 9.6 The Group ofConnected Components of a Néron Model -- 9.7 Rational Singularities -- 10. Néron Models of Not Necessarily Proper Algebraic Groups -- 10.1 Generalities -- 10.2 The Local Case -- 10.3 The Global Case.
Record Nr. UNINA-9910972120703321
Bosch Siegfried  
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1990
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui